In this correspondence, we show that orthogonal expansions of recurrent signals like electrocardiograms (ECG’s) with a reduced number of coefficients is equivalent to a linear time-variant periodic filter. Instantaneous impulse and frequency responses are analyzed for two classical ways of estimating the expansion coefficients: inner product and adaptive estimation with the LMS algorithm. The o...

This paper presents a necessary and sufficient condition for the factorizability of higher order spectra of complex signals. Such a factorizability condition can be used to test if a complex signal can modelize the output of a linear and time invariant system driven by a stationary non gaussian white input. The condition developped here is based on the symmetries of higher order spectra and on ...

We consider the problem of change-point estimation of the instantaneous phase of an observed time series. Such change points, or phase shifts, can be markers of information transfer in complex systems; their analysis occurring in geology, biology and physics, but most notably in neuroscience. We develop two non-parametric approaches to this problem: the cumulative summation (CUSUM) and phase de...

—A time-frequency approach for improved instantaneous frequency estimation of noisy signals has been proposed. This approach is based on the averaged multiple time-frequency distribution obtained by using L-spectrograms with different values of the scaling parameter L. The L-spectrogram with low value of L is characterized by large bias and low variance, while higher L decreases the bias and in...

Abstract: Time-frequency distributions have been used to provide high resolution representation in a large number of signal processing applications. However, high resolution and accurate instantaneous frequency (IF) estimation usually depend on the employed distribution and complexity of signal phase function. To ensure an efficient IF tracking for various types of signals, the class of complex...

Fully 3-D phase-unwrapping algorithms are commonly based on the central assumption that the phase difference between neighbouring sample points in any dimension is generally less than half a phase cycle (the Nyquist criteria). In the case of InSAR time series, however, signals are correlated spatially but uncorrelated over the repeatpass time, due chiefly to changes in atmospheric delay. Here I...

Abstract: The Hilbert transform is a well-known tool of time series analysis that has been widely used to investigate oscillatory signals that resemble a noisy periodic oscillation, because it allows instantaneous phase and frequency to be estimated, which in turn uncovers interesting properties of the underlying process that generates the signal. Here we use this tool to analyze atmospheric da...

We propose a new method for the reconstruction of the Fourier phase of a complex LTI system based on the principal arguments of any pair of horizontal consecutive bispectrum slices of the system output. Since principal bispectrum arguments only are required, there is no need for two-dimensional phase unwrapping. The reconstructed phase diiers from the true one by a constant, integer multiples o...

In time-frequency analysis Hilbert transformation is used to define analytic signals based on which meaningful instantaneous amplitude and instantaneous frequency are defined. In relation to this background we study characteristic properties of the real-valued measurable functions ρ(t) and θ(t), t ∈ R, such that H(ρ(·) cos θ(·))(t) = ρ(t) sin θ(t), ρ(t) ≥ 0, where H is the Hilbert transformatio...